# Operators on spaces of analytic functions

Studia Mathematica (1994)

- Volume: 108, Issue: 1, page 49-54
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topSeddighi, K.. "Operators on spaces of analytic functions." Studia Mathematica 108.1 (1994): 49-54. <http://eudml.org/doc/216039>.

@article{Seddighi1994,

abstract = {Let $M_z$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that $M_z$ is polynomially bounded if $∥M_p∥ ≤ C∥p∥_G$ for every polynomial p. We give necessary and sufficient conditions for $M_z$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.},

author = {Seddighi, K.},

journal = {Studia Mathematica},

keywords = {spaces of analytic functions; polynomially bounded; multipliers; spectral properties; cyclic subspace; operator of multiplication; finite-codimensional invariant subspaces},

language = {eng},

number = {1},

pages = {49-54},

title = {Operators on spaces of analytic functions},

url = {http://eudml.org/doc/216039},

volume = {108},

year = {1994},

}

TY - JOUR

AU - Seddighi, K.

TI - Operators on spaces of analytic functions

JO - Studia Mathematica

PY - 1994

VL - 108

IS - 1

SP - 49

EP - 54

AB - Let $M_z$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that $M_z$ is polynomially bounded if $∥M_p∥ ≤ C∥p∥_G$ for every polynomial p. We give necessary and sufficient conditions for $M_z$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.

LA - eng

KW - spaces of analytic functions; polynomially bounded; multipliers; spectral properties; cyclic subspace; operator of multiplication; finite-codimensional invariant subspaces

UR - http://eudml.org/doc/216039

ER -

## References

top- [1] G. Adams, P. McGuire and V. Paulsen, Analytic reproducing kernels and multiplication operators, Illinois J. Math. 36 (1992), 404-419. Zbl0760.47010
- [2] H. Hedenmalm and A. Shields, Invariant subspaces in Banach spaces of analytic functions, Michigan Math. J. 37 (1990), 91-104. Zbl0701.46044
- [3] S. Richter, Invariant subspaces in Banach spaces of analytic functions, Trans. Amer. Math. Soc. 304 (1987), 585-616. Zbl0646.47023
- [4] D. Sarason, Weak-star generators of ${H}^{\infty}$, Pacific J. Math. 17 (1966), 519-528. Zbl0171.33704
- [5] K. Seddighi and B. Yousefi, On the reflexivity of operators on function spaces, Proc. Amer. Math. Soc. 116 (1992), 45-52. Zbl0806.47026
- [6] H. Shapiro, Reproducing kernels and Beurling's theorem, Trans. Amer. Math. Soc. 110 (1964), 448-458. Zbl0147.11403
- [7] A. Shields and L. Wallen, The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788. Zbl0207.13801
- [8] A. M. Sinclair, Automatic Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge Univ. Press, 1976. Zbl0313.47029

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.